Function parameters, inputs, sensitivities

[DavidMStraub]

Hi,

I think it's great how input parameters and sensitivities can be used for parameter optimization, like in this notebook.

However, I would sometimes like to get the sensitivities with respect to a quantity that is used inside a function parameter, for instance,

• coefficients parametrizing the OCP as function of stoichiometry
• an Arrhenius activation energy or overall factor of an exchange-current density
• ...

Am I right in assuming that this would require rewriting the model/submodel such that the quantity I want to get the sensitivity for is a proper, scalar pybamm.Parameter? For instance, if I wanted to use a function for "Electrolyte conductivity [S.m-1]", say

def my_kappa_e(c_e, T):
    a * c_e

and want the sensitivity w.r.t. a (silly example ...), would the best approach be to monkey-patch LithiumIonParameters.kappa_e_dimensional to return `

pybamm.Parameter("a") * self.c_e

rather than

pybamm.FunctionParameter("Electrolyte conductivity [S.m-1]", inputs)

? Am I on the right track?

[valentinsulzer]

You're on the right track but it's easier than that, you can use pybamm expressions inside the functions in the parameter set so just do

def kappa(c_e, T):
    return pybamm.InputParameter("a") * c_e

parameter_values.update({"Electrolyte conductivity [S.m-1]": kappa})